A single loudspeaker may create sound at both ears of a listener. For example, a loudspeaker on the left side of a listener will still generate some sound at the right ear of the listener. The objective of a crosstalk canceler is to allow production of sound at one of the listener's ears without generating sound at the other ear. This isolation allows any arbitrary sound to be generated at one ear without bleeding to the other ear. Controlling sound at each ear independently can be used to create the impression that the sound is coming from a location away from the loudspeaker.
In principle a crosstalk canceler requires only two speakers (i.e., two degrees of freedom) to control the sound at two ears separately. Many crosstalk cancellers control sound at the ears of a listener by compensating for effects generated by sound diffracting around the listener's head, commonly known as Head Related Transfer Functions (HRTFs). Given a right audio input channel dR and a left audio input channel dL, the crosstalk canceler may be represented as:
      [                                        f            R                                                            f            r                                ]    =                    [        H        ]            ⁡              [                  H                      -            1                          ]              ⁡          [                                                  d              R                                                                          d              L                                          ]      
In this equation, the transfer function of the listener's head due to sound coming from the loudspeaker H is compensated for by the inverse of the transfer function H−1 to produce a right output channel fR and a left output channel fL at the right and left ears of the listener, respectively. Many crosstalk cancelers that use only two speakers suffer from ill-conditioning at some frequencies. For example, the loudspeakers in these systems need to be driven with large signals to achieve crosstalk cancellation and are very sensitive to changes from ideal. In other words, if the system is designed using an assumed transfer function H representing propagation of sound from the loudspeakers to the listener's ears, small changes in H can cause the crosstalk canceler to stop working One example of this is when the transfer function H is measured in an anechoic environment (i.e., no acoustic reflections), but is then implemented in a real room where there are many reflections.